This section reviews the construction of a stratified-smooth universal
deformations for stable (pseudo)holomorphic maps. The proof relies on
a gluing theorem, of the sort given by Ruan-Tian [1]}; our
approach follows that of McDuff-Salamon [2]} who treat the
genus zero case. A different set-up for gluing is described in
Fukaya-Oh-Ohta-Ono [3]}, and explained in more detail in
Abouzaid [4]}. The gluing construction gives rise to charts
for the moduli space of regular stable maps.
